8 September 1993 Transonic airfoil thickness variation requirements for maintaining shock-free flow
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The volume of certain types of smart materials proposed for the coating of aerodynamic surfaces can be instantaneously affected if subjected to an electric or a magnetic field, thus creating dramatic changes in the entire flow field. For example, a transonic airfoil that was designed to be shock-free at a given angle of attack and a given flight Mach number will start developing shock waves immediately after either the angle of attack or the flight Mach number are perturbed. In order to maintain the same aerodynamic performance of an airfoil (that is, maintain the identical distribution of surface pressures on the airfoil) over a range of flight speeds, the airfoil shape must readjust continuously. Using our highly accurate and proven transonic airfoil design code we have performed a detailed evaluation of the required local thickness alterations necessary to maintain the shock-free flow field at different flight Mach numbers. A recommendation as to the required volumetric change of the smart skin materials to be used for the continuous shape adjustments of the aerodynamic configurations was established.
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Helmut Sobieczky, Helmut Sobieczky, George S. Dulikravich, George S. Dulikravich, } "Transonic airfoil thickness variation requirements for maintaining shock-free flow", Proc. SPIE 1917, Smart Structures and Materials 1993: Smart Structures and Intelligent Systems, (8 September 1993); doi: 10.1117/12.152751; https://doi.org/10.1117/12.152751

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